A boat can go across a lake of length I and return in time To at a speed yo. On a rough day there is a uniform current moving with a speed y to help onward journey and impede the return journey. If the time taken to go across and return on the rough day is` t/(t_0)` then the ratio is :

Options

A. `1-(v^(2))/(v_(0)^(2))`
B. `(1)/(1-(v^(2))/v_(0)^(2))`
C. `1+(v^(2))/(v_(0)^(2))`
D. `(1)/(1+(v^(2))/v_(0)^(2))`

Answer

b

Explanation

Here `t_0=(2l)/(v_0)` and `t=(l)/(v_0+v)+(l)/(v_0-v)`
or `t=((v_0-v)l+(v_0+v)l)/(v_0^2 -v^2)=(2lv_0)/(v_0^2-v^2)`
`=(1)/(1-(V^2/v_0^2))`